What is the general solution for sin(x)+sin(x)=2 ?

The general solution for sin(x)+sin(x)=2 is x= pi/2+2pin

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sin(x)+sin(x)=2

sin (x) + sin (x) = 2

x = \frac{π}{2} + 2 πn

Degrees

x = 9 0^{\circ} + 36 0^{\circ} n

Solution steps

sin (x) + sin (x) = 2

Simplify

sin (x) + sin (x) : 2 sin (x)

sin (x) + sin (x)

Add similar elements:

sin (x) + sin (x) = 2 sin (x)

= 2 sin (x)

2 sin (x) = 2

Divide both sides by

2

2 sin (x) = 2

Divide both sides by

2

\frac{2 sin ( x )}{2} = \frac{2}{2}

Simplify

sin (x) = 1

sin (x) = 1

General solutions for

sin (x) = 1

sin (x)

periodicity table with

2 πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

x = \frac{π}{2} + 2 πn

x = \frac{π}{2} + 2 πn

cos (θ) = \frac{1}{6}

sin (x) - 3 cos (x) = 2

(sin (x) - 1) (sin (x) - 3) = 0

x, sin (x) + y^{2} = 4

4 tan^{2} (θ) = - 3 tan (θ) + tan^{2} (θ)

What is the general solution for sin(x)+sin(x)=2 ?
The general solution for sin(x)+sin(x)=2 is x= pi/2+2pin